Ra101 exam 1
Biconditional
A compound statement made up of two conditionals—one indicated by the word "if" and the other indicated by the phrase "only if."
What is a Conjunction?
A compound statement that has two distinct statements (called conjuncts) connected by the dot symbol.
What is a Disjunction?
A compound statement that has two distinct statements (called disjuncts) connected by the wedge symbol.
Argument
A group of statements in which the conclusion is claimed to follow from the premise(s)- Arguments can have more than one premise but only one conclusion
Inferential claim
A passage makes an inferential claim when it expresses a reasoning process
Statement
A sentence that is either true or false
Compound statement
A statement that has at least one simple statement and at least one logical operator as components.
Self-contradiction
A statement that is necessarily false.
Tautology
A statement that is necessarily true.
Substitution instance
A substitution instance of a statement occurs when a uniform substitution of statements for the variables results in a statement. A substitution instance of an argument occurs when a uniform substitution of statements for the variables results in an argument.
Modus ponens
A valid argument form (also referred to as affirming the antecedent).
Modus tollens
A valid argument form (also referred to as denying the consequent).
Truth table
An arrangement of truth values for a truth-functional compound proposition that displays for every possible case how the truth value of the proposition is determined by the truth values of its simple components.
Fallacy of affirming the consequent
An invalid argument form; it is a formal fallacy.
Fallacy of denying the antecedent
An invalid argument form; it is a formal fallacy.
Well-formed formula
Any statement letter standing alone, or a compound statement such that an arrangement of operator symbols and statement letters results in a grammatically correct symbolic expression.
Truth value
Every statement has a truth value (either true or false)
What is a Conditional statement:?
In ordinary language, the word "if" typically precedes the antecedent of a conditional statement, and the statement that follows the word "then" is referred to as the consequent.
Argument form
In propositional logic, an argument form is an arrangement of logical operators and statement variables such that a uniform substitution of statements for the variables results in an argument.
Statement form
In propositional logic, an arrangement of logical operators and statement variables such that a uniform substitution of statements for the variables results in a statement.
Simple statement
One that does not have any other statement or logical operator as a component.
Logical operators
Special symbols that are used to translate ordinary language statements. • The basic components in propositional logic are statements.
Noncontingent statements
Statements such that the truth values in the main operator column do not depend on the truth values of the component parts.
Contingent statements
Statements that are neither necessarily true nor necessarily false (they are sometimes true, sometimes false).
Proposition
The information content or meaning of a statement.
Main operator
The operator that has the entire well-formed formula in its scope.
Order of operations
The order of handling the logical operators within a truth-functional proposition; it is a step-by-step method of generating a complete truth table.
Scope
The statement or statements that a logical operator governs.
Truth-functional proposition
The truth value of any compound proposition using one or more of the five operators is a function of (that is, uniquely determined by) the truth values of its component propositions.
Inconsistent statements
Two (or more) statements that do not have even one line on their respective truth tables where the main operators are true (but they can be false) at the same time.
Consistent statements
Two (or more) statements that have at least one line on their respective truth tables where the main operators are true.
Contradictory statements
Two statements that have opposite truth values under the main operator on every line of their respective truth tables.
Logically equivalent statements
Two truth-functional statements that have identical truth tables under the main operator.
What is a Inclusive disjunction?
When we assert that at least one disjunct is true, and possibly both disjuncts are true. Given this, an inclusive disjunction is false when both disjuncts are false, otherwise it is true.
What is a Exclusive disjunction?
When we assert that at least one disjunct is true, but not both. In other words, we assert that the truth of one excludes the truth of the other. Given this, an exclusive disjunction is true when only one of the disjuncts is true, otherwise it is false.
Sufficient condition
Whenever one event ensures that another event is realized.
Necessary condition
Whenever one thing is essential, mandatory, or required in order for another thing to be realized.
Logic
the systematic use of methods and principles to analyze, evaluate, and construct arguments